PSLE An open rectangular box is shown.
- The inside of the box including the base is painted. Find the painted area.
- When the box is packed full with 1-cm cubes, how many cubes are there?
- How many cubes touch inside the box as a result?
(a)
2 painted areas lengthwise
= 2 x 29 x 45
= 2610 cm2
2 painted areas breadthwise
= 2 x 25 x 45
= 2250 cm
2
Base painted area
= 29 x 25
= 725 cm2
Painted areas
= 2610 + 2250 + 725
= 5585 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 29 x 25 x 45
= 32625 cm
3 Number of 1-cm cubes in the box when full
= 32625 ÷ 1
= 32625
(c)
Number of cubes that touch the base of the box
= 29 x 25
= 725
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (45 - 1) x 29
= 2 x 44 x 29
= 2552
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (25 - 2) x (45 - 1)
= 2 x 23 x 44
= 2024
Number of cubes that touch the inside of the box
= 725 + 2552 + 2024
= 5301
Answer(s): (a) 5585 cm
2; (b) 32625; (c) 5301